If this were a different sort of world, we would all know Hania Zlotnik's name. Instead, we know the name of the guy who judges the singing contests on TV.

Ms. Zlotnik, a tough-talking Mexican who lives in New York, is the person responsible for keeping track of the entire human population.

When we say that the world currently has 6,796,500,000 people, or when we point out that, as of 2007, there were more urbanites than country-dwellers in the world, or that the average human lifespan has jumped from 45 years a century ago to 67 today, we are unknowingly citing Ms. Zlotnik's work as head of the United Nations Population Division.

When I called her the other day, she was in no mood for statistical badinage. Her latest work has found that the world is at a turning point. A decade ago, her office projected that the world population will peak at nine billion in 2050. That's remained accurate, but she told me she's really worried that we've stopped caring.

"People are always quoting that nine-billion figure as if God had declared that the world is going to grow to that size." Of course, it was a projection and, like all projections, it was based on a set of assumptions. "What worries me now is that some fertility rates aren't declining as fast as they should. The decline has started, but a few very poor countries are standing in the way. It could be a big problem."

The world population is not a matter of abstract forces and uncontrollable factors. It has ceased to be an explosive problem because, during my lifetime, most of the world's countries have implemented successful family-planning policies.

"The reason the population of the world is as low as it is today, even though it is not as low as it should be, is because at least 80 per cent of the population of the world is living in the 70 per cent of countries that have had a very important decline of fertility, mostly driven by very successful family-planning programs."

There are about 50 countries that still have large family sizes; a third of them have large populations and no family-planning programs at all. These include the extremely poor countries of southern Africa that have few resources to change things. But they also include Nigeria and Pakistan, two only somewhat poor countries that should be doing better.

After all, Bangladesh, a much poorer country, was able to slash its average family size from six children to three (and it's still falling). Iran cut its average family size from eight children in the 1980s to 1.7 today, a size similar to Canada's. That's how fast things can change.

The nine-billion figure is known as the median projection. Ms. Zlotnik's "high projection" looks at what would happen if the average world family size was higher, by 0.5 children per family. In that case, the world population would hit almost 11 billion in 2050, and keep growing at an exponential rate, passing 40 billion in the following century.

In the "low projection," with 0.5 fewer children per family, it would peak not long after 2040, at not much more than seven billion people - a number and a date that will be economically, socially and ecologically far easier for the world to manage.

Poor-country governments tend to dismiss population growth: After all, what's a 3-per-cent annual growth rate when you're worried about starvation? But if your money is earning 3 per cent interest, it doubles in 24 years; the same applies to people.

"Everything concentrates on those countries," Ms. Zlotnik says. "It is only one-fifth of the world population that is lagging behind. But what I can say as a demographer and even just as an accountant is that, if that group of countries continues to grow at the rates they're growing today, if there's no change in the future, they could repopulate the whole world several times over."

The solution is outlandishly simple. Mexico, Ms. Zlotnik's home country, did it successfully in less than a decade: You send out teams to villages who explain not how to cut family sizes (an abstract concept) but how to widen the space between children - a concrete act that both parents and children appreciate. Four years between kids, rather than four months, opens up a new world. "It is the process that starts the change in society. It's the moment when poor families notice they can do better for their children if they have fewer children."

With that simple lesson, and a few simple devices distributed at clinics, the whole country's population starts falling. And then the world's. And then all our talk about poverty, inequality, food and warming becomes a lot simpler.

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